Problem replicating Mandelbulb power 2

[makc]

I have a problem replicating Mandelbulb power 2 using formula from skytopia site:



Here's what I have:

<a href="http://vimeo.com/moogaloop.swf?clip_id=10556096&amp;server=vimeo.com&amp;fullscreen=1&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=01AAEA" target="_blank">http://vimeo.com/moogaloop.swf?clip_id=10556096&amp;server=vimeo.com&amp;fullscreen=1&amp;show_title=1&amp;show_byline=1&amp;show_portrait=0&amp;color=01AAEA</a>
^{(if this doesn't work when you read this, just take my word that it's really different, and remind me never use vimeo again)}

The code I use is:

      while ((r < 2)&&(i < N)) {

         double theta = atan2( sqrt(x*x + y*y), z);
         double phi = atan2(y, x);
         r = sqrt (x*x + y*y + z*z);
         double rn = pow (r, n);
         x = x0 + rn * sin(theta*n) * cos(phi*n);
         y = y0 + rn * sin(theta*n) * sin(phi*n);
         z = z0 + rn * cos(theta*n);
         // I used to have "r = ..." line here, and thought this caused the glitch
         // however, when I moved it up there, animation (and resulting shape)
         // changed very insignificantly
         //r = sqrt (x*x + y*y + z*z);

         i++;

Earlier I runned it with n=8 and got results that look correct, but apparently the error is there too, just less noticeable.

Can anyone spot my mistake here? Thanks.

[makc]

I just found this thread in povray archives where people had the same problem and the same shape I am getting. It appears, the error is in mandelbulb formula itself

[KRAFTWERK]

I am no mathematician, but I have been asking the same questions and it looks like you have the "cosine" version there


and you aim for the "original sine" version.



More variations in this thread:

http://www.fractalforums.com/theory/summary-of-3d-mandelbrot-set-formulas/

[makc]

yes, that was the one, thanks!



^{still ugly as hell though...}

[KRAFTWERK]

It is a harder beast to render than the power 8 one... lots of irregularities and noise...


Here is one of my renderings with Subblues pixelbender script:


High res:

http://fc02.deviantart.net/fs70/f/2010/060/b/3/DeathStar_Bulb_Power2_by_MANDELWERK.jpg

[bib]

Yes it's always difficlut to properly render the power 2, there too many chaotic shapes and calculation artifacts. When I saw this post I wanted to try again, so I did this image called "Elephant Canyon". Nothing very original, but I like it


http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1993

[KRAFTWERK]

Beautifully sliced bib!